The room temperature charges by a small amount from `T` to `T+DeltaT` (on Kelvin scale). The fundamental frequency of organ pipe changes from `f` to `f+Deltaf`, then

Options

A. `(DeltaT)/(T)`
B. `1/2(DeltaT)/(T)`
C. `2(DeltaT)/(T)`
D. `(-DeltaT)/(T)`

Answer

B

Explanation

`v prop sqrtT " and " n prop sqrtT`
`(n+Deltan)/(Deltan) = sqrt((T+DeltaT)/(T))`
`(n+Deltan)/(Deltan) = (1+(DeltaT)/(T))^(1/2)`
`1+(Deltan)/(n) = 1+1/2 (DeltaT)/(T)`
`(Deltan)/(n) = 1/2 (DeltaT)/(T)`